The instructional situations in which mathematics teachers provide substantive feedback

Feedback provided by mathematics teachers usually addresses procedural skills and, to a much lesser extent, other competencies such as conceptual understanding or engagement in mathematical practices. As most previous literature has studied feedback provided on homework or video prompts, how teachers provide such feedback in the classroom is poorly understood. Here, sixteen lessons taught by five teachers were purposefully sampled from a larger video study (172 lessons) as lessons with high-quality feedback according to a standardized observation instrument. The analysis focused on the instructional situations in which teachers provided feedback. When teachers provided procedural feedback, the situations were orderly and effective. Feedback on conceptual understanding and mathematical practices was provided in situations when students were especially challenged, and entailed a series of complex decisions, thereby placing demands on the teachers to manage both the students’ understanding and behavior. We argue that researchers should focus on how teachers and students negotiate the instructional situation to allow for feedback on conceptual understanding or mathematical practices.

Strange Days: Creating Flexible Pedagogies for Technical Communication

The COVID-19 pandemic created major disruptions in technical communication classrooms everywhere. Although technical communication instructors are used to teaching in a variety of contexts and settings, adopting a flexible approach in the first place will allow them to be better prepared for the changing dynamics of an unpredictable world. The authors present an approach that constructs pedagogical scaffolding to emphasize outcomes, interactions, relationships, and projects. These interrelated aspects form a coherent vision that can support both pedagogical planning and real-time decision making in specific instructional situations.

Using Instructional Design Goals to Appropriately Classify Instructional Design Models

This chapter probes an assertion by Gustafson and Branch (2007) that it is easier to classify instructional models when guided by the needs that call for them. If this is so, identifying appropriate instructional design models for various instructional situations can be greatly simplified. Gustafson and Branch (1997) note that each of the numerous instructional models targets one or more of three types of instructional situations: the Classroom, Product, and Systems situations. In evaluating the assertion, the chapter examines pertinent questions that look at some assumptions guiding the choice of instructional models, the three design situations identified, and some characteristics that separate the various design instances. In the end, it becomes obvious that the instructional design professional will do a better job of classifying instructional models based on a thorough understanding of instructional situations and guided by characteristics of the situation.

A “Sweet” Activity to Teach Basic Population Estimation Principles, Community Diversity Assessment, and Mathematical Reasoning to Biology Students

In this article, we describe how to utilize differently colored M&M candies to represent species within a simulated biological community, and obtain population and diversity estimates utilizing Lincoln-Petersen and Shannon-Weaver methods, respectively. Through use of this activity, our students gain a better understanding of mathematical applications in biological research, and are exposed to basic census and community analysis techniques utilized by practicing biologists. Additionally, this activity may be utilized in various instructional situations where, otherwise, it might prove impractical to take students on a fieldtrip to allow practice of these procedures.

Learning from the Unknown Student

Three instructional situations demonstrate the value of using an “unknown” student's work to allow the advancement of students' mathematical thinking as well as their engagement in the mathematical practice of critiquing the reasoning of others.

Toma de decisiones preinteractivas de profesores de educación física (Planning Decisions of Physical Education Teachers)

Cuarenta y seis profesores participaron en el estudio. Entre ellos, 27 teniendo una experiencia de enseñanza de más de cinco años (12mujeres y 15 hombres) y 19 principiantes (12 mujeres y 7 hombres). Contestaron a cinco escenarios en el marco de una entrevista requerían de decisiones a medio plazo.. Se recogieron y analizaron 434 propuestas de acción dado que una respuesta podía tener muchas propuestas diferentes. Las acciones propuestas fueron analizadas desde registros audio de las entrevistas con profesores. Fueron clasificadas de una manera inductiva. Las opiniones de los profesores con experiencia, hombres y mujeres, son más diversas que aquéllas de sus colegas principiantes, como lo atestigua el gran número de categorías diferentes. Cuatro categorías de decisiones tratan del contenido de la enseñanza: «adaptación de los ejercicios al alumno», «creación de grupos de niveles», «gradación de la dificultad», «misma actividad para todos.» Los profesores interrogados disponen inmediatamente de estrategias disponibles para tratar las diferencias individuales de los alumnos. Según sus características personales, los profesores sugieren preferentemente intervenciones específicas.Abstract: Forty-six PE teachers participated in the study. Among them, 27 had an experience of more than five years in teaching (12 women and15 men) and 19 beginning teachers (12 women and 7 men). Teachers were presented five scenarios of instructional situations. They were asked to readeach scenario and write a response detailing how they would react if the situation occurred during their teaching. Four hundred thirty-four proposalsof actions were gathered and analysed since an answer could have many different proposals. The actions proposed were analysed from audiotapes ofteachers’ interviews. They were classified according to an inductive technique. The opinions of experienced teachers, men and women, differed thanthose of their beginning colleagues, as indicated by the number and content of categories. Four categories of decisions dealt with the content ofeducation: «adaptation of the exercises to the student», «creation of levels groups», «gradation of the difficulty», and «same activity for all.» Theteachers had strategies immediately available to deal with the students’ individual differences. According to their personal characteristics, experiencedteachers displayed a greater variety of application of sound principles of teaching.

Using Instructional Design Goals to Appropriately Classify Instructional Design Models

This chapter probes an assertion by Gustafson and Branch (2007) that it is easier to classify instructional models when guided by the needs that call for them. If this is so, identifying appropriate instructional design models for various instructional situations can be greatly simplified. Gustafson and Branch (1997) note that each of the numerous instructional models targets one or more of three types of instructional situations: the Classroom, Product, and Systems situations. In evaluating the assertion, the chapter examines pertinent questions that look at some assumptions guiding the choice of instructional models, the three design situations identified, and some characteristics that separate the various design instances. In the end, it becomes obvious that the instructional design professional will do a better job of classifying instructional models based on a thorough understanding of instructional situations and guided by characteristics of the situation.

Getting Past Our Assumptions about Web 2.0 and Community Building

While many social media technologies present opportunities to create Networked Knowledge Communities (NKCs), hierarchies among users, content managers, and programmers persist. In the classroom, instructors must manage these power dynamics, yet few have been trained to critically examine technological programs’ affordances to see how they foster community or not. The authors examine a blog assignment for a pedagogy course in which students, after posting several entries, are required to analyze the class’s blog usage to address whether a community was formed through the social media. Through a quantitative and qualitative analysis of the blog assignment the authors learned that while several students claim that the limited number of interactive posts resulted because the instructor did not model community-forming behaviors, community is too complex to impose upon a group. As a result, the authors conclude that instructors, as “programmers” of the rhetorical and instructional situations, need to design and articulate the desired outcomes of community building.

The Influence of Cognitive Styles on Learners’ Performance in e-Learning

This chapter focused the influence of cognitive styles on learners’ performance in e-Learning. The author examined the existing practice of style matching where instructional conditions were matched with learners’ cognitive styles and found that style matching did not necessarily provide learning gains for learners with different cognitive styles. Instead, he proposed ability building as an effective approach to improve learners’ learning. Following the same line, the author further examined the relationship between cognitive styles and instructional situations where situated learning was implemented. The results revealed that instructional situations can significantly influence learners’ learning in complex learning and that cognitive style was not, as viewed by many people, a linear relationship between style and performance. Instead, it displayed multi-dimensional relationships with variables related to e-Learning. The author thus suggested that cognitive style should be examined in a broader manner where variables related to e-Learning be considered simultaneously.